Integers

Presentation

•

Mathematics

•

Practice Problem

•

Hard

Jbryan Jbryan

FREE Resource

52 Slides • 59 Questions

Integers

What are integers?

Include all Whole Number and their OPPOSITES
Integers DO NOT include fractions, or decimals

What are opposites?

The opposite number, is a number that is the same distant from zero on the number line in the opposite direction.

Zero is neither positive or negative and does not have an opposite.

WHAT IS AN INTEGER?

An integer is any WHOLE NUMBER (Positive or Negative) and Zero.

Multiple Select

CHOOSE ALL INTEGERS.

-2.7

$\frac{3}{4}$

-10

Absolute Value

Is how many spaces a number is from zero.
It is always POSITIVE
It is annotated by |#|

Additive Inverses

Numbers that have the same absolute value but opposite signs.
eg. -11 and 11 are additive inverses
The sum of additive inverses is always ZERO
eg: -11 + 11 = 0

Multiple Select

Pick ALL the correct statements:

$\left|5\right|=-5$

Additive Inverse of 7 is -7 $\left|-10\right|=10$

Absolute Value of 5 is 5

Additive Inverse of 3 is 3

undefined

Multiple Choice

What is the opposite of -10?

$\frac{1}{10}$

$\frac{10}{1}$

Multiple Choice

What number is the opposite of -7?

-7

Multiple Choice

5 $>$ -5

5 $<$ -5

5 $=$ -5

5 $\ge$ -5

Multiple Choice

-9 $<$ -18

-9 $>$ -18

-9 $\cong$ -18

-9 $\le$ -18

Multiple Choice

-21 $>$ -17

-21 $\ge$ -17

-21 $\le$ -17

-21 $<$ -17

Multiple Choice

-21 $>$ -17

-21 $\ge$ -17

-21 $\le$ -17

-21 $<$ -17

Multiple Choice

-12 $=$ 12

-12 $\ge$ 12

-12 $<$ 12

-12 $\cong$ 12

Multiple Choice

What is your basis to get the symbol of the sum?

Bigger number

Smaller number

Multiple Choice

How would you represent 500 ft below sea level

$\frac{1}{500}$

500

-500

Multiple Choice

How would you represent the absolute value of -23?

$\left|-23\right|=-23$

$\left|-23\right|=0$

$\left|-23\right|=23$

$\left|-23\right|=\left|23\right|$

Multiple Select

When could you use negative numbers in real life?

Money

Distance

Temperature

Height

Additive Inverses

Numbers that have the same absolute value but opposite signs.
eg. -11 and 11 are additive inverses
The sum of additive inverses is always ZERO
eg: -11 + 11 = 0

Multiple Select

Pick ALL the correct statements:

$\left|5\right|=-5$

Additive Inverse of 7 is -7 $\left|-10\right|=10$

Absolute Value of 5 is 5

Additive Inverse of 3 is 3

undefined

To Add Integers

Same signs ADD and keep the sign
Different signs SUBTRACT and take the sign of the bigger number

Multiple Choice

Evaluate the following: $-3\ +\ \left(-8\right)$

-5

-11

Multiple Choice

Evaluate the following: $-2+5$

-7

-3

5 + 9 = ?

32 + 41 = ?

16 + 21 = ?

-1

Multiple Choice

6 + 2

(-6) + 2

6 + (-2)

(-6) + (-2)

Multiple Choice

6 + 4 = 10

(-6) + 2 = -4

6 + (-4) = -2

6 + (-4) = 2

Fill in the Blanks

What is the sum of 12 + (-4)?

Fill in the Blanks

What is the sum of -105 + 67?

Multiple Choice

Find the sum of 64 + (-38)

102

-102

-26

Multiple Choice

Answer the following:

1. (-67) + (-24)=

-91

-43

+91

+43

Multiple Choice

2. (+45) + (+98) =

+53

+143

-53

-143

Rule No. 1:

To add integers having the same signs, add the numbers and copy the common sign to the sum.

Illustrative Examples

1. (+13) + (+34) =

Solution:

+1 3

+ +3 4

+4 7 The sum is +47 or 47 since the common sign is positive (+).

Examples

2. (-411) + (-234) =

Solution:

-4 1 1

+ -2 3 9

-6 5 0 The sum is -650 since the common sign is negative (-).

Multiple Choice

Answer the following:

1. (-67) + (-24)=

-91

-43

+91

+43

Multiple Choice

2. (+45) + (+98) =

+53

+143

-53

-143

Rule No. 2:

To add integers having different signs, disregard first the signs and subtract the numbers. Then, copy the sign of the greater number to the final answer. (Note: Disregard also the sign in identifying the greater number.)

Illustrative Example

1. (-56) + (+24) =

Solution:

(-5 6)

+ (+2 4)

-3 2 The final answer is -32. The sign is negative (-) since the sign of the greater number which is 56 is negative.

Multiple Choice

Answer the following:

1. (-89) + (+24)=

-65

-78

+65

+78

Multiple Choice

2. (+75) + (-13) =

- 28

-62

+65

+62

Multiple Choice

Answer the following:

1. (-89) + (+24)=

-65

-78

+65

+78

SUBTRACTION OF INTEGERS

Mastery of addition of intergers is a pre-requisite on this lesson.

SUBTRACTION OF INTEGERS

To subtract integers, change the sign of the subtrahend and proceed to addition process.

SUBTRACTION OF INTEGERS

Example 1: Solve : 18 - ( - 21 )

Multiple Choice

Find the difference : $45\ -\ \left(-93\right)$

$-138$

$-48$

$48$

$138$

Fill in the Blanks

$Solve:\ 98\ -\ \left(-74\right)$

Type answer...

SUBTRACTION OF INTEGERS

Example 2: Solve : - 54 - ( - 33 )

Fill in the Blanks

$-104\ -\left(-189\right)$

Type answer...

Multiple Choice

$-78\ -\ \left(-54\right)$

$-132$

$-24$

$24$

132

SUBTRACTION OF INTEGERS

Example 3

SUBTRACTION OF INTEGERS

Example 3

Multiple Choice

$-71\ -\ 82$

$-9$

$-\ 153$

$153$

$9$

Fill in the Blanks

$-115\ -\ 324$

Type answer...

THANK YOU!!!

Image on intro slide: www.pexels.com, creator: Black Ice

THANK YOU!!!

Image on intro slide: www.pexels.com, creator: Black Ice

- 6 - (-4) = -2 0r -6 - (-2) = -4

-2 + -4 = -6

Subtraction is an Opposite of addition

Subtraction of Integers

4 + 6 = 10

10 - 6 = 4 or 10 - 4 = 6

Subtraction is an Opposite of addition

Subtraction of Integers

10 minuend

- 6 subtrahend

4 difference

Change the operation to addition and then change the sign of the subtrahend.

+ -6

or 10 + -6 = 4

Subtraction of Integers: keep, change, change

Subtraction of Integers

1. Keep the first number ( minuend).

2. Change the minus sign to plus sign.

3. Change the last number ( subtrahend) to its opposite

4. Add the integers

-10 - 4 =

- 10 + (-4) = - 14

You may use the number line to solve/ to find the answer. Check my screen and observe.

Multiple Choice

Negative number + Negative number =

postive number

negative number

zero

Multiple Choice

-9 + (-5)

-14

-4

Multiple Choice

-14 + (-3)

-17

-11

Multiple Choice

Is the answer to -23 + 34 is .....

negative

positive

Multiple Choice

7 + (-3) = ?

-4

-10

Multiple Choice

2 + (-8) = ?

-16

-6

Multiple Choice

-5 + 9 = ?

-4

-14

Subtracting Integers

We will rewrite all problems to addition to make it easier!
REMEMBER: SAME, Change, OPPOSITE
Keep the first number the same!
Change the subtraction sign to addition
Write down the opposite number!

Multiple Choice

Using additive inverse, write this problem as an addition problem.

-22 - (-7)

-22 + 7

-22 + (-7)

22 + 7

22 + (-7)

Multiple Choice

Which question is the SAME as
-4 - (-2) ?

-4 + 2

-4 - 2

4 + 2

4 - 2

Multiple Choice

How would you rewrite -10 - 5?

10 + (-5)

-10 + 5

-10 + (-5)

10 + 5

Multiple Choice

$-7-3$

$4$

$-4$

$-10$

$10$

Multiple Choice

solve the following problem.

(-15) - (-5)

-10

-2

-23

-7

Multiple Choice

3 -9

-12

-6

Week 2 Assignments!

IXL lessons! C.9 and B.6
Week 2 Video: Watch in class Wednesday/Thursday
Quiz has been posted. Take on Friday!

Week 2 Assignments!

IXL lessons! C.9 and B.6
Week 2 Video: Watch in class Wednesday/Thursday
Quiz has been posted. Take on Friday!

Let's Review Adding Integers!

Keep the sign and add their absolute values

-5 + -7 = -12

5 + 7 = 12

Same Signs

Multiple Choice

Evaluate -50 + -25

-75

-25

Fill in the Blanks

Evaluate -8 + -8

Type answer...

Let's Review Adding Integers!

Determine which number has the biggest absolute value. That will be the sign of your final answer. Then, subtract the absolute values of your integers.

12 + -7 = 5

-15 + 10 = -5

-20 + 10 = -10

Different Signs

Multiple Choice

Evaluate -6 + 8

-14

-2

Fill in the Blanks

Evaluate 10 + -15

Type answer...

Now Let's Learn How to

Subtract Integers!

Keep the sign of the first number.
Change the subtraction sign to an addition sign.
Change the sign of the last number to its opposite.
Follow the addition rules.

-10 - 5 ----> -10 + -5 = -15

Keep Change Opposite -----> KCO

100

Subtraction is the Adding the Opposite.

Let's try these together....

1) 6 - 9

2) -9 - 4

3) -8 - 10

Keep Change Opposite -----> KCO

101

Multiple Choice

How do you rewrite 6 - 12 using KCO?

-6 - 12

6 + -12

6 - -12

-6 - -12

102

Multiple Choice

Now evaluate 6 - 12

-18

-6

103

Multiple Choice

Evaluate 5 - 7

-2

-12

104

Subtracting a Negative is like Adding a Positive

If it's getting less cold, it's warming up.

If you are getting less negative, you are getting more positive.

If you owe less money, you are increasing in wealth.

10 - -2 ----> 10 + + 2 = 12

105

Subtracting a Negative is like Adding a Positive

Let's try these together...

1) 9 - - 10

2) -5 - -4

3) -8 - -12

Keep Change Opposite -----> KCO

106

Multiple Choice

How would you rewrite 9 - -3 using KCO?

9 - 3

-9 - 3

9 + + 3

-9 + 3

107

Fill in the Blanks

Evaluate 9 - - 3

Type answer...

108

Fill in the Blanks

Evaluate -10 - 3

Type answer...

109

Fill in the Blanks

Evaluate -9 - 3

Type answer...

110

Fill in the Blanks

-15 - -5

Type answer...

111

You are on a hike 120 feet above sea level. Your camping site is at 10 feet below sea level. How far apart are you from your camping site? Draw a picture/number line to help you think through this situation.

120 - -10 =

Real World Problem

Integers

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